Dynamics of fluctuations at multicritical points

V. Dohm

Amnon Aharony A

István A. Kovács

Quantum multicritical points (QMCPs) emerge at the junction of two or more quantum phase transitions due to the interplay of disparate fluctuations, leading to novel universality classes. While quantum critical points have been well characterized, our understanding of QMCPs is much more limited, even though they might be less elusive to study experimentally than quantum critical points. Here, we characterize the QMCP of an interacting heterogeneous quantum system in two and three dimensions, the ferromagnetic random transverse-field Ising model (RTIM). The QMCP of the RTIM emerges due to both geometric and quantum fluctuations, studied here numerically by the strong disorder renormalization group method. The QMCP of the RTIM is found to exhibit ultraslow, activated dynamic scaling, governed by an infinite disorder fixed point. This ensures that the obtained multicritical exponents tend to the exact values at large scales, while also being universal---i.e., independent of the form of disorder---providing a solid theoretical basis for future experiments.

Pierre Le Doussal, A. Brooks Harris

The renormalization-group recursion relations obtained by Chen and Lubensky for the multicritical point associated with simultaneous critical fluctuations in both the spin-glass and ferromagnetic order are reanalyzed. To first order in \ensuremath{\epsilon}==6-d we find that the multicritical fixed point is located inside the Nishimori manifold and that the scaling axes agree with those obtained recently from general arguments. It is confirmed that the scaling along the Nishimori line and at the paramagnetic-spin-glass transition are related. We also point out some universal properties of the multicritical point of possible experimental interest.

J. P. Stark

Yukiyasu Ozeki, Nobuyasu Ito

Exact dynamical properties are discussed for the ± J Ising model around the multicritical point (MCP). It is found that the relation of relaxations between the non-equilibrium remanent magnetization m ( t ) and the equilibrium autocorrelation function q ( t ) at the MCP is different from that at the pure critical point. The dynamic critical exponent for the ferromagnetic ordering defined by and that for the spin glass ordering defined by become identical at the MCP. Accurate numerical calculations for them are performed in two and three dimensions using the non-equilibrium relaxation analysis. The MCP is located at and the exponent is estimated as for the square lattice. They are estimated as and for the simple cubic lattice.